GNU MPFR 3.1.3: Miscellaneous Functions
Description: How to install and use GNU MPFR, a library for reliable multiple precision floating-point arithmetic, version 3.1.3.

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### 5.12 Miscellaneous Functions

Function: void mpfr_nexttoward (mpfr_t x, mpfr_t y)

  If x or y is NaN, set x to NaN. If x and y are equal, x is unchanged. Otherwise, if x is different from y, replace x by the next floating-point number (with the precision of x and the current exponent range) in the direction of y (the infinite values are seen as the smallest and largest floating-point numbers). If the result is zero, it keeps the same sign. No underflow or overflow is generated.

Function: void mpfr_nextabove (mpfr_t x)
Function: void mpfr_nextbelow (mpfr_t x)

  Equivalent to `mpfr_nexttoward` where y is plus infinity (resp. minus infinity).

Function: int mpfr_min (mpfr_t rop, mpfr_t op1, mpfr_t op2, mpfr_rnd_t rnd)
Function: int mpfr_max (mpfr_t rop, mpfr_t op1, mpfr_t op2, mpfr_rnd_t rnd)

  Set rop to the minimum (resp. maximum) of op1 and op2. If op1 and op2 are both NaN, then rop is set to NaN. If op1 or op2 is NaN, then rop is set to the numeric value. If op1 and op2 are zeros of different signs, then rop is set to −0 (resp. +0).

Function: int mpfr_urandomb (mpfr_t rop, gmp_randstate_t state)

  Generate a uniformly distributed random float in the interval 0 <= rop < 1. More precisely, the number can be seen as a float with a random non-normalized significand and exponent 0, which is then normalized (thus if e denotes the exponent after normalization, then the least -e significant bits of the significand are always 0).

  Return 0, unless the exponent is not in the current exponent range, in which case rop is set to NaN and a non-zero value is returned (this should never happen in practice, except in very specific cases). The second argument is a `gmp_randstate_t` structure which should be created using the GMP `gmp_randinit` function (see the GMP manual).

  Note: for a given version of MPFR, the returned value of rop and the new value of state (which controls further random values) do not depend on the machine word size.

Function: int mpfr_urandom (mpfr_t rop, gmp_randstate_t state, mpfr_rnd_t rnd)

  Generate a uniformly distributed random float. The floating-point number rop can be seen as if a random real number is generated according to the continuous uniform distribution on the interval [0, 1] and then rounded in the direction rnd.

  The second argument is a `gmp_randstate_t` structure which should be created using the GMP `gmp_randinit` function (see the GMP manual).

  Note: the note for `mpfr_urandomb` holds too. In addition, the exponent range and the rounding mode might have a side effect on the next random state.

Function: int mpfr_grandom (mpfr_t rop1, mpfr_t rop2, gmp_randstate_t state, mpfr_rnd_t rnd)

  Generate two random floats according to a standard normal gaussian distribution. If rop2 is a null pointer, then only one value is generated and stored in rop1.

  The floating-point number rop1 (and rop2) can be seen as if a random real number were generated according to the standard normal gaussian distribution and then rounded in the direction rnd.

  The third argument is a `gmp_randstate_t` structure, which should be created using the GMP `gmp_randinit` function (see the GMP manual).

  The combination of the ternary values is returned like with `mpfr_sin_cos`. If rop2 is a null pointer, the second ternary value is assumed to be 0 (note that the encoding of the only ternary value is not the same as the usual encoding for functions that return only one result). Otherwise the ternary value of a random number is always non-zero.

  Note: the note for `mpfr_urandomb` holds too. In addition, the exponent range and the rounding mode might have a side effect on the next random state.

Function: mpfr_exp_t mpfr_get_exp (mpfr_t x)

  Return the exponent of x, assuming that x is a non-zero ordinary number and the significand is considered in [1/2,1). The behavior for NaN, infinity or zero is undefined.

Function: int mpfr_set_exp (mpfr_t x, mpfr_exp_t e)

  Set the exponent of x if e is in the current exponent range, and return 0 (even if x is not a non-zero ordinary number); otherwise, return a non-zero value. The significand is assumed to be in [1/2,1).

Function: int mpfr_signbit (mpfr_t op)

  Return a non-zero value iff op has its sign bit set (i.e., if it is negative, −0, or a NaN whose representation has its sign bit set).

Function: int mpfr_setsign (mpfr_t rop, mpfr_t op, int s, mpfr_rnd_t rnd)

  Set the value of rop from op, rounded toward the given direction rnd, then set (resp. clear) its sign bit if s is non-zero (resp. zero), even when op is a NaN.

Function: int mpfr_copysign (mpfr_t rop, mpfr_t op1, mpfr_t op2, mpfr_rnd_t rnd)

  Set the value of rop from op1, rounded toward the given direction rnd, then set its sign bit to that of op2 (even when op1 or op2 is a NaN). This function is equivalent to `mpfr_setsign (rop, op1, mpfr_signbit (op2), rnd)`.

Function: const char * mpfr_get_version (void)

  Return the MPFR version, as a null-terminated string.

Macro: MPFR_VERSION
Macro: MPFR_VERSION_MAJOR
Macro: MPFR_VERSION_MINOR
Macro: MPFR_VERSION_PATCHLEVEL
Macro: MPFR_VERSION_STRING

  `MPFR_VERSION` is the version of MPFR as a preprocessing constant. `MPFR_VERSION_MAJOR`, `MPFR_VERSION_MINOR` and `MPFR_VERSION_PATCHLEVEL` are respectively the major, minor and patch level of MPFR version, as preprocessing constants. `MPFR_VERSION_STRING` is the version (with an optional suffix, used in development and pre-release versions) as a string constant, which can be compared to the result of `mpfr_get_version` to check at run time the header file and library used match:

      if (strcmp (mpfr_get_version (), MPFR_VERSION_STRING))
        fprintf (stderr, "Warning: header and library do not match\n");

  Note: Obtaining different strings is not necessarily an error, as in general, a program compiled with some old MPFR version can be dynamically linked with a newer MPFR library version (if allowed by the library versioning system).

Macro: long MPFR_VERSION_NUM (major, minor, patchlevel)

  Create an integer in the same format as used by `MPFR_VERSION` from the given major, minor and patchlevel. Here is an example of how to check the MPFR version at compile time:

      #if (!defined(MPFR_VERSION) || (MPFR_VERSION<MPFR_VERSION_NUM(3,0,0)))
      # error "Wrong MPFR version."
      #endif

Function: const char * mpfr_get_patches (void)

  Return a null-terminated string containing the ids of the patches applied to the MPFR library (contents of the `PATCHES` file), separated by spaces. Note: If the program has been compiled with an older MPFR version and is dynamically linked with a new MPFR library version, the identifiers of the patches applied to the old (compile-time) MPFR version are not available (however this information should not have much interest in general).

Function: int mpfr_buildopt_tls_p (void)

  Return a non-zero value if MPFR was compiled as thread safe using compiler-level Thread Local Storage (that is, MPFR was built with the `--enable-thread-safe` configure option, see `INSTALL` file), return zero otherwise.

Function: int mpfr_buildopt_decimal_p (void)

  Return a non-zero value if MPFR was compiled with decimal float support (that is, MPFR was built with the `--enable-decimal-float` configure option), return zero otherwise.

Function: int mpfr_buildopt_gmpinternals_p (void)

  Return a non-zero value if MPFR was compiled with GMP internals (that is, MPFR was built with either `--with-gmp-build` or `--enable-gmp-internals` configure option), return zero otherwise.

Function: const char * mpfr_buildopt_tune_case (void)

  Return a string saying which thresholds file has been used at compile time. This file is normally selected from the processor type.

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